Rather remake. Remaster on current old engine is very hard to do as Brevik said, also they will have problems in stopping modders (tmc/map hack), dupers and overall cheaters (botters are impossible to stop), next problem is very archaic game mechanics which only small group of hc fans want to play nowadays.
They firstly announced WC3hd so it looks like they have much of work on D2HD already. This new WC3 Reforge looks like semi Remake (some differences in Campaign but the same MP), new President is "u think u do, but u dont" so I think D2hd will be full remake with different systems, maybe with boa and ah to bring back d3 ppl, mobile ppl, new casual ppl and ocasionally d2 hc ppl. It will be big test (like "diablo" mobile) before new Diablo 4 game.
You are absolutely right. It's impossible to remake D2 while keeping all of its systems and mechanics because of issues that you have already listed.
I like the idea of bringing it back with BOA / AH, it might work out... Although I'm sure that anything other than the original trading system will create a huge backlash but some things are just not going to happen i.e bringing back the game with all the bots, dupes, hacks, real money 3rd party sites, etc, etc...